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Quest to Compute Pi

Updated: Dec 24, 2018


Pi is one of the most interesting numbers in mathematics. Ever since Archimedes calculated Pi in 250 BC, mathematicians have been kept intrigued and busy by this magic number Pi.


There is also some sort of elegance in the Greek letter. This symbol was first used by William Jones. The Swiss mathematician, Leonhard Euler, popularized the use of this symbol.


Babylonians first approximated the value of Pi to be 3.125. Egyptians computed it as 256/81 or 3.16. Archimedes was the first one to come up with a theoretical, rather than measured, value of Pi. At the age of 23, Aryabhata, a 5th-century mathematician from India, computed the value of Pi to be 62832/20000 or 3.1416. In the same century, Chinese mathematicians approximated Pi to 7 digits. In 1340 AD, Madhav, an Indian Mathematician, came up with Pi accurate up to 11 digits. In the 18th century, a French mathematician, George Buffon calculated the value of Pi based on probability. The quest for a more accurate value of Pi continued as we will see in the later part of this article.


In 1897, Dr. Edwin Goodwin, a mathematician from Indiana, tried to redefine the value of Pi to 3. The house bill number 246 was passed in the Indiana State Legislature in 1897. It was because of the efforts by Dr. Waldo, a mathematics professor at Purdue University, that the bill was stopped in the Senate.

In 1914, Ramanujan, the Indian mathematician, came up with a formula that converges rapidly. The formula is:

The Ramanujan’s infinite series for pi was modified by Chudnovsky brothers in 1989. The variation looks like as follows.

They used IBM3090 supercomputer and with the above formula, they computed Pi to over 1 billion decimals.


The quest for computing Pi to higher digit accuracy continues. The latest record is Peter Trueb, in 2016, computed 22 trillion digits!


Our new blog is named to honor all those mathematicians who put in tremendous efforts to compute Pi. Going forward, we plan to discuss various technologies related to data. In the upcoming blogs, we will discuss topics such as face detection, performance characterization, digital simulators, as well as warranty analytics. Hope you enjoy the blog. Your suggestions are most welcome.


References:

  1. Ramanujan’s Formula for Pi, https://crypto.stanford.edu/pbc/notes/pi/ramanujan.html

  2. Pi in Indian Mathematics, Sourav Roy, January 7,2011, https://souravroy.com/2011/01/07/pi-in-indian-mathematics/

  3. "House Bill No. 246, Indiana State Legislature, 1897" by Will E. Edington in Proceedings of the Indiana Academy of Science, 1935

  4. A Brief History of π, https://www.exploratorium.edu/pi/history-of-pi

  5. Wikipedia, https://en.wikipedia.org/wiki/pi



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